We now apply the CPMG sequence to detect a sinusoidal magnetic field. The calculation of the decoherence under the pulse sequence is done in a slightly different manner. To do so, we use the general formalism outlined in [1]}, [2]} giving us \(\nu =exp[-(\frac{N^{1-s}}{2T_2f})^p]\) , where \(s\)  is set by the noise spectrum of the decohering bath. For our use case of an electronic spin bath, this can be approximated as \(2/3\)  [3]}. \(T_2\)  is the coherence time equal to 53 \(\mu \) s, and, as before, \(f\)  represents the frequency of the magnetic field and \(N\)  is the number of pulses applied. Our results are shown in Figs.REF -REF  where we see an actual increase in the confidence as well as longer lasting confidence measurements as a function of time.
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